# Conformal Mapping of Simple Non-Convex Polygon onto Unit Circle

I have seen conformal mappings from convex polygons to the unit circle, and I have seen mappings from the circle to non-convex polygons. I have not seen arbitrary simple non-convex polygons mapped to unit circles, which is where my interest lies.

Does such a mapping exist? In either case, what is an example, and what is a specific reference that I can follow up with?

• Isn't this precisely what Riemann mapping theorem says? en.wikipedia.org/wiki/Riemann_mapping_theorem – xyzzyz Aug 14 '17 at 18:24
• Certainly the inverse of such a mapping exists by RMT, so you should be able to compute it somehow – DaveNine Aug 15 '17 at 0:43